Final answer:
The reasonable estimates for 472 ÷ 6 are 480 divided by 6 and 450 divided by 3, as they are the quotients closest to the actual division result when compared to the given options.
Step-by-step explanation:
To select all the reasonable estimates for 472 ÷ 6, we must find quotients that are close to the result of this division. Since 1,200 divided by 6 equals 200, which is a known fact and given here for reference, we can use it to check the reasonableness of other estimates.
- 450 divided by 5 = 90 (Not reasonable; too low compared to 200)
- 480 divided by 6 = 80 (Reasonable; very close to 472 ÷ 6)
- 500 divided by 5 = 100 (Not reasonable; too low compared to 200)
- 450 divided by 3 = 150 (Reasonable; somewhat close to 472 ÷ 6)
- 1,200 divided by 6 = 200 (Provided as reference)
Therefore, the quotients that are reasonable estimates for 472 ÷ 6 are 480 divided by 6 and 450 divided by 3.